This
is an interesting paper in an area that needs more research, namely, how
children perform in economic games. The typical questions go as follows: Are children
altruistic? Are they selfish?

The authors review and criticize some of the relevant previous
research. Murnighan & Saxon (1998) found that kindergartners
made larger ultimatum offers and accepted smaller ultimatum offers of candy
than did third or sixth graders. However, Lucas et. al argue that Murnighan & Saxon’s results are probably not valid
since they use a kind of simulated game, in which the child is asked to imagine
that another child offers such and such amount of candy (instead of actually
playing the ultimatum game). They also quote Harbaugh, Krause, & Liday (2003), who found that seven-year olds made and accepted
smaller ultimatum proposals than adults; and Hill and Sally (2006), who found
that 6-year-olds already make offers as fair as those of adults after repeated rounds
of play. Benenson, Pascoe and Radmore (2007), on the other hand, found that very
young children can be altruistic when playing dictator (4-year-olds donated, on
average, 25% of a stake of ten stickers to another classmate).

The authors also mention a
problem with some of the previous research: often, researchers make children
play with tokens that have no inherent value; children are explained that they
will be able to trade the tokens for other stuff later. Lucas et al. argue that
researchers should use items with tangible, real value for children, such as
candy, stickers or toys, since the use of “symbolic” tokens poses additional
cognitive demands on children and might affect experimental results.

Lucas et al. found, in their own study, that children made,
on average, offers of 4.7 stickers in the ultimatum game and 3.99 stickers in
the dictator game. That is, children seem to be making quite fair offers.

It is well established that adults give an average of 40% of
the money at stake in ultimatum. But there is a big difference between the 4-year-olds’
47% and the adults’ 40%. In adults, the mode
(i.e., the most frequent answer) is 50%, while some adults give 40%, 30% or
less, and almost no one offers more than 50%. However, some of Lucas el al.’s
4-year-olds offer more than 50%. They
call this phenomenon hyperfair offers.
There is a qualitative difference between adults and children: adults oscillate
between the fair (“half and half”) and the strategic (“less than half”). Many children,
by way of contrast, offer more than is
fair, more than half the stake.

“(…) the percentage of hyperfair offers (…) increased from
18% in the dictator game to 33% in the ultimatum game. Adults, in contrast,
almost never make hyperfair offers (only 3.5% of offers in Lucas, Et al., (2007)
were hyperfair).”

Lucas et al. also report that, in their study, children did
not seem to take into account the behavior of the other player in their
responses, even if it was unfair. In the dictator game, children did not change
the amount of their offer in response to receiving either a low or fair offer
from the friend. Children’s offers for the second game were also not affected
by whether the friend had accepted or rejected the child’s first offer.

The results of the dictator game suggest that children in the
sample are quite altruistic: “The adult average offer of 20% of the stake in
the dictator game (Camerer, 2003) is usually interpreted as evidence that
individuals have preferences for altruism, since proposers could offer less in
a dictator game without fear of rejection. With an average offer in the
dictator game of 40% of the stake, our sample of children made more altruistic
offers than adults.”

Children’s average offer of 4 stickers (or 40% of the stickers
at stake) doubles adults’ typical offer of 20% of the money at stake in dictator,
and does not seem to far away from the 47% children offered in the ultimatum
game. How do Lucas et al. explain these data? “(Children’s) ability to perform
a cost/benefit analysis was limited. They did not seem to appreciate the degree
to which they could “shade” their offers without penalty.” Thus, Lucas et al.
are assuming that children have the desire or goal of keeping as many stickers
as possible but they that their strategic thinking is deficient. “Children were
more generous than they needed to be and were limited in their ability to act
strategically in bargaining games in order to maximize their own benefits while
avoiding the costs of rejection.”

Lucas et al.’s conclusion: “children are quite altruistic”, “they
may have an innate sense of fairness and altruism.” This result is, in my
opinion, over-simplistic. Previous research in economic psychology has
established that adults are altruistic and fair to some degree, but also a little
bit selfish and strategic. Lucas et al. assume, therefore, that either children
are born altruistic, fair and strategic or they learn these behaviors along the
way. If research shows that children are completely selfish, then altruism is
learned. If it shows they are altruistic from the start, then it must be
innate.

I quote them: “We predicted that children would perform
similarly to adults in showing preferences for fairness and altruism.
Alternatively, and as some others have found, children could be less fair,
indicating that fairness must be learned over the course of development.”

They start with a binary opposition between selfishness and
altruism. In this approach, learning is seen as lineal, cumulative, unidirectional.
They start with some innate concepts and, while learning, children simply absorb
information from their milieu or copy adult models, until they reach the end-point.

There are other possibilities, however. For example: young children
might be neither selfish nor altruistic. They might be following other types of
reciprocity not related to the fair, contract-like, 50/50 reciprocity of
adults. They might use an associative reciprocity of the kind “I give a lot of
stickers to the other kid because I like to make friends” (see Faigenbaum, 2005), that are typical of children’s peer cultures
and of exchanges within the family. Such an approach dispels the apparent inconsistencies
of previous research: it’s not just that children are not yet able to think “strategically”.
They are not even interested in this kind of reasoning.

Associative reciprocity might explain why kindergartners make
large ultimatum offers and accepted small ultimatum offers of candy (Murnighan & Saxon, 1998) or why 4-year-olds can be so
altruistic when playing dictator (Benenson,
Pascoe and Radmore, 2007). It might also explain the results of Lucas et al.’s
own research, for example, why children give 40% of the stake in the dictator
game.

Rose, C. M. (2007). The Moral Subject of Property. William and Mary Law Review, 48(5), 1897–1926.

In this beautifully written article, Carol Rose makes the argument that although property arrangements might seem unfair or unjust in many respects (how it is acquired, how it is distributed across society, its effect on the commoditization of sacred or moral aspects of social life), the institution of property is nevertheless beneficial for society at large insofar as it creates stability and incentives for individuals to take care of their property, invest, trade and create more value for society at large in the long run. So even when arrangements are not perfect in many specific cases (because they have morally questionably implications), it’s better to tolerate these shortcomings and to apply the established rules of ownership acquisition and distribution, because “property, as an institution, requires stability in people’s expectations about their own and other people’s claims.”

The article also contains a couple of nice quotes about one of my favorite topics: the relationship between associative and strict reciprocity: “Gift exchange cements community bonds-from a community of two on up to many more-keeping all the participants in a vague but nevertheless socially and emotionally charged condition of mutual give and take.” “(…) Gift giving differs from market exchange because through gifts, each party engages in imaginative participation in the life of the other, helping to cement relationships.”

I had a stimulating discussion with a neuroscientist the other day. I tried to explain to her that my interest in children’s cognitive development is linked to my interest in epistemology, that is, to what I refer to in this blog as the normativity of thought.

For example, I argue that researchers who try to explain children’s knowledge of math from a nativist point of view, can only explain the starting point of cognitive development. The starting point is innate mathematical knowledge, which is mostly implicit, and basically consists in an ability to identify the numerosity of collections of objects found in the outside world. In other words: researchers have shown that animals (humans included) have the innate ability to assess the size of a collection of perceived objects (for example, they can notice that a collection of 15 pebbles is greater than a collection of 10 pebbles). They can also discriminate among exact quantities, but only when dealing with small sets (two, three, and perhaps four objects). Also, some animals and human babies can perform elementary arithmetic operations on small sets (adding two plus one, subtracting one from two, etc.) I am referring here to studies by Dehaene (2011), Izard, Sann, Spelke, & Streri (2009), Spelke (2011), and many others.

This basic capacity is certainly different from fully-fledged “human math.” The latter involves, at the very least, the symbolic representation of exact numbers larger than three. We (humans) can represent an exact number by saying its name (“nine”), or by using a gesture that stands for the number in question (depending on the culture, this might be done by touching a part of one’s body, showing a number of fingers, etc. – see Saxe ( 1991) and also http://en.wikipedia.org/wiki/Chinese_number_gestures). And, of course, we can write down a sign that represents the number (for example, with using the Arabic numeral “9”).

Scholars agree on the fact that advanced math is explicit and symbolic, and that it builds on (and uses similar brain areas to) its precursor, innate math. Once they operate on the symbolic level, humans can do things like: performing operations (addition, subtraction, multiplication, division, and others), demonstrating mathematical propositions, proving that one particular solution to a mathematical problem is the correct one, etc. To sum up: our symbolic capacities allow us to re-describe our intuitive approach to math on a precise, normative, epistemic level.

Now, here’s when it gets tricky. I argue that the application of algorithms on the symbolic level is not merely mechanical. Humans are not computers applying rules from a rule book, one after the other (like Searle in his Chinese room). Rather, as Dehaene (2011) argues, numbers mean something for us. “Nine” means nine of something (anything). “Nine plus one” means performing the action of adding one more unit to the set of nine units. There is a core of meaning in innate math; and this core is expanded and refined in our more advanced, symbolic math.

When executing mathematical operations (either in a purely mental fashion, or supported by objects) one gets a feeling of satisfaction when one arrives to a right (fair, correct, just) result. Notice the normative language we apply here (fair, correct, right, true, just). We actually experience something similar to a sense of justice when both sides of an equation are equal, or when we arrive to a result that is necessarily correct. (Note to myself: talk to Mariano S. We might perhaps do brain fMRIs and study if the areas of the brain that get activated by the “sense of justice” in legal situations, also light up when the “sense of justice” is reached by finding the right responses in math. If a similar region gets activated, that might suggest that there is a normative aspect to math that corresponds to the normative aspect of morality).

For me, then, the million dollar question is: how do humans go from the implicit, non-symbolic, automatic level to the explicit, symbolic, intentional and normative level? What is involved in this transition? What kind of biological processes, social experiences and individual constructions are necessary to achieve the “higher,” explicit level? (These are interesting questions both for the field of math and for the field of morality). And my hypothesis is that this transition necessarily demands the intervention of a particular type of social experience, namely, the experience of the normative world of social exchanges and rules of ownership (I’ve talked a little about such reckless hypotheses in other posts of this blog).

Now, when I try to explain all this to the neuroscientist, I lose her. She doesn’t follow me. For her, human knowledge is the sum of a) innate knowledge and b) learning from the environment. Learning is the process by which our brain acquires new information from the world, information that was not pre-wired, that didn’t came ready to use “out of the box.” Whether such learning involves a direct exposure to certain stimuli that represent contents (a school teacher teaching math to his or her students) or a more indirect process of exposure to social interactions is not an interesting question for her. It doesn’t change her basic view according to which there are two things, and two things only: innate knowledge and acquired knowledge. What we know is the result of combining the two. And this is the case both for humans and for other animals. Period.

Something similar happens when I talk to her about the difference between “cold processing” and “hot processing.” We were discussing the research I am conducting right now. I interview children about ownership and stealing. In my interview design, children watch a movie where one character steals a bar of chocolate from another, and eats it. The interviewer then asks the child a series of questions aimed at understanding her reasoning about ownership and theft. Now, the movie presents a third person situation. This means that the child might be interested in the movie, but he or she is not really affected by it. Children reason about what they see in the movie, and sometimes they seem to say what they think it’s the appropriate thing to say, echoing adults’ discourse. Because, after all, the movie is fiction, not the real world.

I believe that normativity emerges not from absorbing social information that comes from external events (watching movies, attending to teachers’ explanations) but from children’s real immersion in first person, real world, conflictive situations. When a child is fighting against another for the possession of a toy, there are cries and sometimes there even is physical violence. These encounters end up in different ways; sometimes children work out a rule for sharing the scarce resource, sometimes they just fight, and sometimes an adult intervenes and adjudicates in the conflict. The child’s reactions during these events is not dictated by cold reasoning but by deeper impulses. It is in these situations where we should look for the emergence of our basic normative categories, such as reciprocity (both social and logical, or “reversibility”), ownership (or the relationship between substance and its “properties”), quantity (used to implement equity and equality), etc.

But, again, my biologist friend does not feel that the distinction between the impulsive, intense, hot reactions we experience when involved in real conflicts and the kind of third person reasoning that is triggered by movies and artificial stimuli is an important one. In both cases, she argues, it’s the same cognitive system that is at work. What we think about third person characters is probably similar to how we reason about ourselves (thanks to our capacity for empathy, our mirror-neurons, etc.)

I don’t know who’s right and who’s wrong here.

Dehaene, S. (2011). The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition. The number sense How the mind creates mathematics rev and updated ed (p. 352). Oxford University Press, USA. Retrieved from http://www.amazon.com/dp/0199753873

I like the summary Erin Robbins and Philippe Rochat wrote for my presentation at the Fairness Conference (Emory University, 2012). It really captures the spirit of what I was trying to convey. It goes as follows:

Gustavo Faigenbaum from the University Autonoma de Entre Rios in Argentina (“Three Dimensions of Fairness”), in contrast to the preceding two evolutionary perspectives, argues that in understanding fairness, individual morality has been overrated and institutions underrated. To this end, Faigenbaum advances several claims that draw from both psychological and philosophical theories. First, he argues that institutional experience shapes concepts of fairness. This is evident in children’s interactions in schoolyards, where they engage in associative reciprocity (sharing with others to build alliances and demonstrate social affinities) rather than strict reciprocity. At the level of adult behavior, this associative reciprocity is also evident in gift-giving rituals. Second, Faigenbaum argues that possession and ownership are the most important institutions in the development of fairness reasoning because they involve abstraction and are the first step in the development of a deontological perspective.

Concepts of morality do not need to be evoked; he argues that research on children’s protests of ownership violations reflect an emphasis on conventional rather than moral rules. Faigenbaum concludes by arguing that participation in rule-governed activities is sufficient to create mutual understandings about what constitutes fair exchange (per philosopher John Searle’s “X counts as Y” rule). Developmental research demonstrates that fairness is an autonomous domain of experience that is fundamentally tied to institutions and cannot be reduced to moral reasoning proper.

My son L. is taking a bath. He’s 3 years – 1 month. After playing around in the water for a while, he says “I’m a fish”. Then looks at me and says: “I am a penguin.” I reply: “Hello, penguin”. He: “Nice to meet you”. Then he adds: “I pay” (extends his hand as if giving me money). I extend my hand and say: “Here is your change.” Then he says: “Here’s a gift” (and again extends his hand). So I say, “Oh, what is it?” He answers: “A perfume”. He then gives me several more presents, sometimes saying that the gift is “a perfume”, and at other times saying it’s “a surprise”.

I find this sequence very interesting. Our interaction comprises a continuous series of conventional behaviors that are typically used to start social exchanges and to keep them alive. So we go from “greetings” to “payment,” and then to “gift-giving”. Children, of course, do not understand payments as a way to deliver a certain amount of monetary value in the context of a sale or some other economic contract. Rather, they ​see payment as a ritualized exchange, in that sense similar to gift-giving or greeting rituals (as we know from the research in the area of children’s economic notions, such as Berti and Bombi’s, Delval’s, Jahoda’s and Danziger’s among many others). All the actions performed by Leon are instances of ritual exchanges, realized with a purely associative purpose, that is: he interacts in order to keep me engaged in interaction.

Just finished reading “Sharing, talking and giving” (Marshall, 1961). Great article. As the author summarizes it: “This paper describes customs, practised by the !Kung Bushmen in the Nyae Nyae region of South Africa, which help them to avoid situations that are likely to arouse ill will and hostility among individuals within the bands and between bands. Two customs which seem to be especially helpful and which I describe in detail are meat-sharing and gift-giving. I mention also the !Kung habits of talking, aspects of their good manners, their borrowing and lending, and their not stealing.”

A couple of details were interesting for me:

Taking possession: When they hunt, “The owner of the animal is the owner of the first arrow to be effectively shot into the animal so that it penetrates enough for its poison to work. That person is responsible for the distribution”. Note: the owner is not the head of the band, or the person who organized the hunt, or the person who shot the arrow. The owner of the animal is the owner of the arrow (who often is not even be part of the hunting expedition). Ownership of the tool (arrow) becomes ownership of the hunted animal.

Associative reciprocity: !Kung Bushmen make presents. And the motives for this “are the same as in gift-giving in general: to measure up to what is expected of them, to make friendly gestures, to win favour, to repay past favours and obligations, and to enmesh others in future obligation. I am sure that when feelings of genuine generosity and real friendliness exist they would also be expressed by giving”. A nice list that sums up what I mean by “associative reciprocity”. As Demi, a !Kung informant, tells the anthropologist: “a !Kung never refuses a gift. And a !Kung does not fail to give in return. Toma said that would be ‘neglecting friendship’.”